NOTE FROM MRS. KEENER:
Point values have increased by 10 points in the rubric. Meaning the most points achievable is 25 due to the time to make a video and embed it. All group members must participate in the video in some way. You are required to post how you contributed to the video below this information. I contributed to the video by being in the video and coming up with some of the ideas for the clips. :)Kourtneyyy
i contributed to the video by being in it and helping to put together the clips for the final video on imovie, john
I contributed to the video by being in the vidwo and filming it as well. In addition to planning some of the action and all that good stuff, zach
I contributed to the video by being in it. Jasmine I Contributed By Filming Part Of The Video And Was In The Beginning. Chris
Chapter 7 Wiki: Powers, Roots, and Radicals
YAY MATH!
What is this chapter about?
What will you learn?
powers
roots
radicals
how to use rational exponets and nth roots of numbers
how to perform operations with and find inverses of functions
how to graph radical functions and solve radical equations
Key Vocabulary nth root of a (p. 401) For an integer n greater than 1, if b^n = a, then b is an nth root of a. index (p. 401) The integer n (greater than 1) in the expression the nth root of a. simplest form (p. 408) a radical expression after you apply the properties of radicals, remove any perfect nth powers, and rationalize any denominators) like radicals (p. 408) Two radical expressions that have the same index and the same radicand.power function (p. 415) A function of the form y = ax^b where a is a real number and b is a rational number. composition (p. 416) The composition of the function f with the function g is h(x) - f(g)(x)). inverse relation (p. 422) A relation that maps the output values of an original relation back to their original input values. The graph of an inverse relation is the reflection of the graph of the original relation. inverse function (p. 422) A relation and its inverse relation whenever both relations are functions. radical functions (p. 431) A function that contains a radical, such as y = the square root of x or y = the cubic root of x.
Section 7.1: nth Roots and Rational Exponents
Evaluate nth rooth.
Using Nth roots in real life.
You can extend the concept of a square root to other types of roots.
If b is > 1, and b^n = a, then b is the nth root of a.
Real Nth Roots
- If n is odd then a has one real nth root.
- If n is even and positive then it has two real nth roots.
- If n is even and = 0 then it has one nth root.
- If n is even and a < 0, then a has no real nth roots.
practice:Evaulate-9^3/2, answer on pg. 401
Section 7.2: Properties of Rational Exponents
Properties of Rational Exponets and Radicals.
The properties of integer exponets can be applied to rational exponets. (See chart on page 407).
practice:Simplify- (8^1/2 x 5^1/3)^2, answer on pg. 407
Section 7.3: Power Functions and Function Operations
Performing function operations.
Using Function Operations in Real Life.
practice:Let f(x)=3x-1 and g(x)=2x-1, find f(f(x)), answer on pg. 416
Section 7.4: Inverse Functions
Finding Inverses of Linear Functions.
practice:Find the inverse of y=2x-4, answer on pg. 422
Section 7.5: Graphing Square Root and Cube Root Functions
Graphing Radical functions.
Using Radical Functions in Real Life.
practice:Describe how to obtain the graph of y= (x+1)^1/2)-3 from the graph of x^1/2, answer on pg. 432
Study Ideas:
Go back and re-read your notes.
Study this wiki and try the practice problems.
Try some odds.
Do the review on page 456 and the test following it.
Look over your 7.1-7.4 test.
Go through everything we've learned this unit, and TEACH it to someone else.
It can be a person, or a dog, or anything you want. Just speak and explain out loud using your own words.
Your understanding will improve dramatically.
Go ask Mrs. Keener for help during her free lunch periods.
Section 7.7: Statistics and Statistical Graphs
practice:What is the symbol for sigma?, answer on pg.446
Real Life Application Problem:
1.) Jake imports furniture from Mexico. The exchange rate is 11.30 pesos per U.S dollar. The cost of each piece of furniture is given in pesos. The total cost of each piece of furniture includes a 15% service charge. A-- Write a function for the total cost in U.S dollars. B-- Write a function for the cost in dollars based on the cost in pesos. (answers given at the bottom)
2.) Radium-226 is a form of radioactive element that decays over time. An inital sample of radium-226 has a mass of 500mg. The mass of radium-226 remaining from the initial sample after "t" years is given by 500 (2 X t/1600). To the nearest miligram, how much radium-226 would be left after 800 years? (answers given at the bottom)
Point values have increased by 10 points in the rubric. Meaning the most points achievable is 25 due to the time to make a video and embed it. All group members must participate in the video in some way. You are required to post how you contributed to the video below this information.
I contributed to the video by being in the video and coming up with some of the ideas for the clips. :)Kourtneyyy
i contributed to the video by being in it and helping to put together the clips for the final video on imovie, john
I contributed to the video by being in the vidwo and filming it as well. In addition to planning some of the action and all that good stuff, zach
I contributed to the video by being in it. Jasmine
I Contributed By Filming Part Of The Video And Was In The Beginning. Chris
Chapter 7 Wiki: Powers, Roots, and Radicals
YAY MATH!
roots
radicals
how to perform operations with and find inverses of functions
how to graph radical functions and solve radical equations
Key Vocabulary
nth root of a (p. 401) For an integer n greater than 1, if b^n = a, then b is an nth root of a.
index (p. 401) The integer n (greater than 1) in the expression the nth root of a.
simplest form (p. 408) a radical expression after you apply the properties of radicals, remove any perfect nth powers, and rationalize any denominators)
like radicals (p. 408) Two radical expressions that have the same index and the same radicand.power function (p. 415) A function of the form y = ax^b where a is a real number and b is a rational number.
composition (p. 416) The composition of the function f with the function g is h(x) - f(g)(x)).
inverse relation (p. 422) A relation that maps the output values of an original relation back to their original input values. The graph of an inverse relation is the reflection of the graph of the original relation.
inverse function (p. 422) A relation and its inverse relation whenever both relations are functions.
radical functions (p. 431) A function that contains a radical, such as y = the square root of x or y = the cubic root of x.
Section 7.1: nth Roots and Rational Exponents
Evaluate nth rooth.
Using Nth roots in real life.
You can extend the concept of a square root to other types of roots.
If b is > 1, and b^n = a, then b is the nth root of a.
Real Nth Roots
- If n is odd then a has one real nth root.
- If n is even and positive then it has two real nth roots.
- If n is even and = 0 then it has one nth root.
- If n is even and a < 0, then a has no real nth roots.
Section 7.2: Properties of Rational Exponents
Properties of Rational Exponets and Radicals.
The properties of integer exponets can be applied to rational exponets. (See chart on page 407).
Section 7.3: Power Functions and Function Operations
Performing function operations.
Using Function Operations in Real Life.
Section 7.4: Inverse Functions
Finding Inverses of Linear Functions.
Section 7.5: Graphing Square Root and Cube Root Functions
Graphing Radical functions.
Using Radical Functions in Real Life.
Study Ideas:
It can be a person, or a dog, or anything you want. Just speak and explain out loud using your own words.
Your understanding will improve dramatically.
REMEMBER THE TEST IS THIS FRIDAY! GOOD LUCK!
Section 7.6: Solving Radical Equations
practice:Solve x^1/3)-4=0, answer on pg. 437
Section 7.7: Statistics and Statistical Graphs
practice:What is the symbol for sigma?, answer on pg.446
Real Life Application Problem:
1.) Jake imports furniture from Mexico. The exchange rate is 11.30 pesos per U.S dollar. The cost of each piece of furniture is given in pesos. The total cost of each piece of furniture includes a 15% service charge. A-- Write a function for the total cost in U.S dollars. B-- Write a function for the cost in dollars based on the cost in pesos. (answers given at the bottom)
2.) Radium-226 is a form of radioactive element that decays over time. An inital sample of radium-226 has a mass of 500mg. The mass of radium-226 remaining from the initial sample after "t" years is given by 500 (2 X t/1600). To the nearest miligram, how much radium-226 would be left after 800 years? (answers given at the bottom)
REAL LIFE APPLICATION PROBLEM ASWERS:
1.) A-- P(c) = c + 0.15c B-- D(c) = c/11.30
= 1.15c
2.) 500 (2 - 800/1600) = 500 (2 ^ - .5) = 500 ( 1/2.5) = 500/ 2.5 ~ 354